# Math Help - Basic Properties of Number (Proof)

1. ## Basic Properties of Number (Proof)

I am not sure where to post this question, but it seems to require only algebra.

The maximum of two numbers x and y is denoted by max(x,y). Thus max(-1,3) = max(3,3) = 3 and max (-1, -4) = max(-4, -1) = -1. The minimum of x and y is denoted by min(x,y). Prove that:

max(x,y) = (x+y+abs(y-x))/2

I was able to prove it if x = y but after that I don't know how to prove it.

Thanks.

2. Break it down into two cases,

what happens when $x \ge y$?
what happens when $x < y$?

3. What about saying that $\frac{x+y+abs(y-x))}{2}=x$.

After some algebra you get that $abs(y-x)=x-y \Rightarrow x\geq y$.

4. Thank you. I will give it another try.